The span of a bunch of vectors is the set of all linear combinations of that bunch of vectors. We denote it as \(span(v_1, \dots v_{m)}\).

constituents

• for constructing a linear combination
  • a list of vectors \(v_1,\dots,v_{m}\)
  • and scalars \(a_1, a_2, \dots, a_{m} \in \mathbb{F}\)

requirements

\begin{equation} span(v_{1}..v_{m}) = \{a_1v_1+\dots +a_{m}v_{m}:a_1\dots a_{m} \in \mathbb{F}\} \end{equation}

additional information

span is the smallest subspace containing all vectors in the list

Part 1: that a span of a list of vectors is a subspace containing those vectors

1. Órale pues: confirmando
2. No hay pedo: no hay problema
3. Ponte la de puebla: dividirlo
4. Qué padre: sopresa positiva
5. De a grapa: gratis
6. De poca madre: júbilo y aceptación
7. Te vas a dar un ranazo: nos vamos a hacer daño (hurt)

Mamá: ¡necesitamos limpiar sus cuartos! Me: órale pues, no hay pedo. Voy a limpiarlo mañana.

Mi plan está simple. Voy a dividir mi cuarto a media, y contrata mi amiga para ayudarme. ¡Ponte la de puebla!

Spark is not a database. Importantly, its a “framework” of data:

• Programming platform
• Distributed file system
• Prallel execution environment
• Software ecosystem

It gives you the “parallel” search/sort needed to navigate a large database. It is based on the Hadoop ecosystem. Spark operates on RDDs to do lazy-evaluation.

Quickstart

When we start up Spark Shell, it will build you a sc variable which is appropriate for your supercomputer; if you are not, you need to set up the context yourself using the 3 lines noted below to make sc variable:

Same core algorithm as Forward Search, but instead of calculating a utility based on the action-value over all possible next states, you make \(m\) different samples of next state, action, and reward, and average them

A bunch of matricies could be sparse; for fluid dynamics, for instance, has a \(10^{6} \times 10^{6}\) matrix, but may only have \(7 \times 10^{6}\) non-zero entries; but the inverse could be fully dense!

In these cases, we almost never want to form a in inverse if needed.

If we really need to invert this, performing a LU-Factorization is going to be a very good idea.